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arXiv · 1806.03099

Positive Functionals and Hessenberg Matrices

J. -B Lasserre·Mihai Putinar
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Abstract

Not every positive functional defined on bi-variate polynomials of a prescribed degree bound is represented by the integration against a positive measure. We isolate a couple of conditions filling this gap, either by restricting the class of polynomials to harmonic ones, or imposing the vanishing of a defect indicator. Both criteria offer constructive cubature formulas and they are obtained via well known matrix analysis techniques involving either the dilation of a contractive matrix to a unitary one or the specific structure of the Hessenberg matrix associated to the multiplier by the underlying complex variable.

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J. -B Lasserre, Mihai Putinar. 2018-06-08. Positive Functionals and Hessenberg Matrices. https://arxiv.org/abs/1806.03099

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